Summary: Discrete Random Functions (DRF) defined over finite and discrete domain and range sets are used to model random finite-gray-scale digital images. The basic characterizing functionals of the theory, their properties and interrelationships are proved and it is shown that these functionals are sufficient for the complete probabilistic specification of DRF. Morphological tools for modeling and analyzing images are also considered. The major contribution of this work is to show that discrete random set formulation for morphological processing of binary images can indeed be generalized and placed in a broader perspective of discrete random function formulation for finite gray-scale images.
For the entire collection see [Zbl 0885.00059].